Correct Delaunay Triangulation in the Presence of Inexact Inputs and Arithmetic

Abstract

The construction of the Delaunay triangulation depends on the correct determination of whether or not a fourth point is inside the circle determined by three other points. By modeling the data points as disks and examining the associated mutual tangent circles, we show how to construct an incircle test that is reliable and sharp, one that is not corrupted by round-off error, one that can deal with inexact input data, avoids rational and big integer arithmetic, and brings geometry to the forefront instead of error analysis or arithmetic.